# An adaptive sum of powered score (SPU) test for gene-set (pathway) and mutiple phenotypes Tests whether gene-set (pathway) is associated with multivariate outcomes; provides a series of p-values of GEE-SPU(pow, pow2, pow3) and GEEaSPUpath tests. ```r GEEaSPUpath(pheno, geno, nSNPs, Z = NULL, corstr = "independence", pow = c(1,2,4,8), pow2 = c(1,2,4,8), pow3 = c(1,2,4,8), n.perm = 1000) ``` ## Arguments - `pheno`: a numeric phenotype matrix with each row as a different individual and each column as a separate phenotype. - `geno`: a numeric genotype matrix with each row as a different individual and each column as a snp; the SNPs (with the number stored in nSNPs) from one gene are stored consecutively from the first gene. - `nSNPs`: A numeric vector, whose length matches to the total number of genes; each element of vector indicate the number of SNPs in each gene. - `Z`: a numeric covariate matrix with each row as a different individual and each column as a covariated to be adjested. - `corstr`: a character string specifying the correlation structure of phenotypes. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured" (default = "independence"). - `pow`: a vector of the power weight to be used at a SNP level (default = c(1,2,4,8)). - `pow2`: a vector of the power weight to be used at a trait level (default = c(1,2,4,8)). - `pow3`: a vector of the power weight to be used at a gene level (default = c(1,2,4,8)). - `n.perm`: a numeric value of number of null statistics (default = 1000). ## Details Adaptive association tests for gene-set (pathway) and multiple phenotypes using GEE. ## Returns a vector of p-values from GEE-SPU(pow, pow2, pow3) tests and GEE-aSPUpath test. ## References Kim J, Zhang Y, and Pan W (2016). "Powerful and adaptive testing for multi-trait and multi-SNP associations with GWAS and sequencing data." **Genetics**, 203(2), 715--731. ## Author(s) Junghi Kim and Wei Pan ## Note GEEaSPUpath function only supports a case for a quantitative trait (model = "gaussian") and a permutation based test (null.type = "perm"). ## Examples ```r # -- simulating phenotypes # -- n.subjects: number of subjects # -- n.traits: number of phenotypes # -- Sigma: covariance matrix of phenotypes (e.g. AR(1)) set.seed(136) n.subjects <- 100 n.traits <- 3 sigma <- 2; rho <- 0.5 Sigma0 <- diag(n.traits) Sigma <- sigma * rho^abs(row(Sigma0) - col(Sigma0)) eS <- eigen(Sigma, symmetric = TRUE) ev <- eS$values X <- matrix(rnorm(n.subjects * n.traits), n.subjects) pheno <- X %*% diag(sqrt(pmax(ev, 0)), ncol(Sigma)) %*% eS$vectors # -- simulating genotype # -- Assume we have two genes each of which has 3 and 5 SNPs respectively. # -- n.geno1: number of SNPs included in the gene1 # -- n.geno2: number of SNPs included in the gene2 # -- nSNPs <- c(3,5) n.geno1 <- 3 n.geno2 <- 5 maf1 <- 0.2 maf2 <- 0.4 gene1 <- matrix(rbinom(n = n.subjects*n.geno1, size = 2, prob = maf1), ncol = n.geno1) gene2 <- matrix(rbinom(n = n.subjects*n.geno2, size = 2, prob = maf2), ncol = n.geno2) geno <- cbind(gene1, gene2) # -- Computing the p-value of GEEaSPUpath test Pvl <- GEEaSPUpath(pheno = pheno, geno = geno, nSNPs = c(3,5), Z = NULL, corstr = "independence", pow = c(1,4,8), pow2 = c(1,4,8), pow3 = c(1,4,8), n.perm = 1000) # -- Each element of Pvl is a p value of GEE-SPU(pow,pow2,pow3) in order # -- The last element of Pvl is a p value of GEE-aSPUpath test Pvl Pvl[length(Pvl)] # > Pvl # SPU.1.1.1 SPU.1.1.4 SPU.1.1.8 SPU.1.4.1 SPU.1.4.4 SPU.1.4.8 SPU.1.8.1 SPU.1.8.4 # 0.00900000 0.05600000 0.07000000 0.06200000 0.08300000 0.11200000 0.06100000 0.08200000 # SPU.1.8.8 SPU.4.1.1 SPU.4.1.4 SPU.4.1.8 SPU.4.4.1 SPU.4.4.4 SPU.4.4.8 SPU.4.8.1 # 0.10600000 0.58100000 0.54300000 0.49200000 0.62400000 0.64000000 0.62700000 0.64900000 # SPU.4.8.4 SPU.4.8.8 SPU.8.1.1 SPU.8.1.4 SPU.8.1.8 SPU.8.4.1 SPU.8.4.4 SPU.8.4.8 # 0.67100000 0.67500000 0.58300000 0.53700000 0.48100000 0.63400000 0.64600000 0.63800000 # SPU.8.8.1 SPU.8.8.4 SPU.8.8.8 aSPUpath # 0.66000000 0.68100000 0.67900000 0.04395604 # > Pvl[length(Pvl)] # aSPUpath # 0.04395604 ```